An economic analysis is presented using the T-Method for a 19-section sample duct system outlined in the Fundamentals Handbook [ASHRAE, 1997 ref152]. The following analyses were done in the following sequence [Tsal et. al., 1998]:
First, the calculation was conducted using T-Method with no optimization for the same air flows, lengths, cross sections, and fittings as presented in the ASHRAE Handbook. A comparison between sectional pressure losses for the T-Method and ASHRAE calculations shows that the results are very close. Slight differences exist because of the interpolation techniques used for the fitting coefficients.
Second, the optimization was performed using the same fan as presented in the Fundamentals Handbook [835 Pa (3.34 in.WG)]. After three iterations, the T-Method presented an optimum pressure distribution between supply and return systems, 465 Pa (1.86 in. WG) and 371 Pa (1.49 in. WG), respectively. The effectiveness of various duct materials, shapes, and sizes was analyzed. The results of this analysis are summarized in Table 1.
Table 1. Results of Duct Optimization: Surfaces and Economic Effect (for equal fan pressure).
| No. Cal |
Duct System Calculation |
Duct Surface, m2 (ft2) | Economic Effect | |
| ASHRAE | T-Method | |||
| 1 | ASHRAE Example | 211.4 (2275) | 0 | |
| 2 | Rectangular & round ducts, before size rounding | 180.0
(1938) |
14.8% | |
| 3 | Rectangular & round ducts: Size rounded 25 mm (1") below 500 mm (20"), 50 mm (2") above 500 mm | 183.2
(1972) |
13.3% | |
| 4 | Rectangular & round ducts,
Size rounded 25 mm (1") |
182.8
(1968) |
13.5% | |
| 5 | Round ducts, before size rounding | 165.6 (1783) | 21.6% | |
| 6 | Round ducts, size rounded 25 mm (1") below 500 mm (20"), 50 mm (2") above 500 mm (20") | 168,2
(1811) |
20.4% | |
| 7 | Round ducts, size rounded 25 mm (1") | 168
(1808) |
20.5% | |
The economic improvements range from 13.3% to 21.6%. What causes such large economic effect for impacts on systems with the same fan pressure? The cause becomes clear once the air velocity differences between the ASHRAE example and the T-Method calculation are analyzed; the velocities in the optimized design are reduced close to the fan (at sections 18 and 19), and the available pressure is then used to increase the air velocity in other sections by reducing duct sizes. The duct sections close to the fan are relatively short [7.5 m (31.1 ft) and 4 m (24.6 ft) but have large fitting coefficients (4.26 and 5.31); therefore, velocities in sections 18 and 19 are reduced drastically from 10.43 m/s (2044 fpm) and 6.13 m/s (1203 fpm) to 4.68 m/s (917 fpm) and 4.05 m/s (795 fpm).
Another factor affecting optimization is pressure distribution between the return and supply subsystems. For the case previously discussed, the pressure differences are summarized in Table 2 below. These differences affect the economics of the solution.
Table 2. Results of Duct Optimization: System Pressure
| Design | Pressure, Pa (in.WG) | ||
| Supply subsystem | Exhaust subsystem | Total | |
| ASHRAE calculation | 488 (1.96) | 344 (1.38) | 832 (3.34) |
| T-Method calculation | 436 (1.75) | 396 (1.59) | 832 (3.34) |
For determining the effect of system optimization in different American cities, a combination of electrical costs for three types of consumers and five duct costs were selected for six cities.
If the same system as presented in the ASHRAE example is designed for a residential building in New York City using spiral galvanized ducts (case 1), fan pressure is 205 Pa (0.82 in.WG) compared to 835 Pa (3.34 in.WG) for the ASHRAE example. In the ASHRAE example, the life-cycle cost for this system is $39,797 including an initial cost of $7,052 and operating costs of $32,745. For the same system calculated using the T-Method, life-cycle cost is $18,544, initial cost is $10,515, and operating cost is $8,030. The maximum economic effect of the T-method on the life-cycle cost is a 53.4 % savings. This result is obtained from 62.1% energy savings after the 8.7% higher initial cost.
If the same system were built in Seattle with industrial electrical rates and stainless steel ductwork (case 11), the T-Method design saves 12.2% of the life-cycle cost, a 16.5% reduction in initial cost and 4.3% increase in energy costs
Table 3. Results of Duct Optimization: Economic Comparison
|
No |
City
Consumer Duct |
Elect.
cost $/kWh |
Duct
cost $/m2 |
Life-Cycle Cost
$ |
Economic Effect
% |
|||
|
ASHRAE |
T-METHOD |
Life-
Cycle Cost |
First-
Cost |
Operating Cost | ||||
| 1 | New York Residential
Spiral ducts |
16.34 |
33.36 |
39,797 |
18,544 |
53.4% |
-8.7 |
62.1 |
| 2 | New York
Commercial Spiral ducts |
15.85 |
33.36 |
38,815 |
18,335 |
52.8% |
-8.6 |
61.4 |
| 3 | San Diego
Industrial Spiral ducts |
11.88 |
33.36 |
30,859 |
16,167 |
47.6% |
-9.0 |
56.6 |
| 4 | Atlanta
Commercial Low press.,bare |
8.52 |
41.01 |
25,743 |
16,288 |
36.7% |
-8.8 |
45.5 |
| 5 | Detroit
Residential Galvan.,Insulat. |
7.26 |
55.43 |
26,267 |
19,061 |
27.4% |
-7.1 |
34.5 |
| 6 | Denver
Industrial Aluminum ducts |
4.83 |
43.27 |
18,826 |
14,219 |
24.5% |
-6.2 |
30.7 |
| 7 | San Diego
Industrial Stainless ducts |
11.88 |
127.9 |
50,862 |
40,020 |
21.3% |
-4.9 |
26.2 |
| 8 | Seattle
Commercial Spiral ducts |
2.4 |
33.36 |
11,862 |
9,764 |
17.7% |
-2.6 |
20.3 |
| 9 | Seattle
Industrial Spiral ducts |
2.03 |
33.36 |
11,120 |
9,374 |
15.7% |
-0.9 |
16.6 |
| 10 | Seattle
Residential Spiral ducts |
1.89 |
33.36 |
10,840 |
9,216 |
15.0% |
-0.1 |
15.1 |
| 11 | Seattle
Industrial Stainless |
2.03 |
127.9 |
31,123 |
27,336 |
12.2% |
16.5 |
-4.3 |
| Average | 7.71 | 54.2 | 26,919 | 18,029 | 29.5% | -3.7 | 33.1 | |
Table 3 shows the results of comparisons between the T-Method and Equal Friction method calculations for different fan pressures and alternative duct materials and electrical costs for a hypothetical system with a total of approximately 185 meters of duct. Differences in life-cycle cost for the Equal Friction designs in this table are due a result only of electricity prices and the unit cost of ducts. This table suggests that, with the T-Method, cost-effective electrical savings of 20% to 40% can typically be achieved over systems designed using traditional methods. Savings of as much as 60% are technically feasible but would be cost effective only if electricity costs are relatively high.
Duct systems calculated by different engineers using the T-Method will result in the same duct sizes and fan pressure requirements. This means the T-Method could make duct design a science rather than an art.
